تعميم المادة والمضادة للمادة من خلال التأثير المترافق

f4402 Geometrization of matter and antimatter through coadjoint action of a group on its momentum space. 3 : Geometrical description of Dirac's antimatter. A first geometrical interpretation of antimatter after Feynmann and so-called CPT-theorem. (p2)
negative energies sectors.
. . Fig.2 **** : Subsequent symmetries

. . Fig.3) : The eight components group its momentum and movement spaces. ** **

...It becomes easy to examine the impact of each component on momentum and movement. We shall consider a reference movement and momentum J+1 , refering to positive energy matter ( the impact on positive energy photons will be analysed in a second step ). The sector of the group in which the element is chose will be grey.

Next, the movements of ordinary matter. l = +1 m = +1 l m = +1

The charges are unchanged. The movement M2 refers to (E>0), positive mass, orthochron matter.

. **Fig.4 ** : Movements of ordinary matter. Action of orthochron elements of the group, with l = 1. Charges unchanged.

**Fig. 5 ** **: Coadjoint action of a ****( **l = -1 ; m = 1 ) element of the group on the momentum **associated to the movement of normal matter : **the new movement corresponds to Dirac's antimatter.

...On the figure 5 the line M1 figures the movement of normal, orthochron matter. We figures straight lines because ou group does not take account of force field, like gravitational or electromagnétic field. It only runs the behaviour of lonely particles, charged mass-points.

...We choose an element in the grey area, corresponding to a ( l = -1 ; m = 1 ) matrix. The ( l = - 1 ) value changes the signs of all the z i. They become negative. The new path is in the second sector, corresponding to antimatter. As l m = - 1 the charges are reversed. But as time is not reversed, the energy and the mass of the particle remains positive. This is a geometric description of ( orthochron ) antimatter after Dirac.